Sato-Tate group search results

Results (1-50 of 155 matches)

 

Label	Wt	Deg	$\mathrm{dim}_{\mathbb{R}}$	$\mathrm{G}^0$	Name	$\mathrm{G}/\mathrm{G}^0$	$\mathrm{Pr}[t\!=\!0]$	$\mathrm{E}[a_1^2]$	$\mathrm{E}[a_1^4]$	$\mathrm{E}[a_1^6]$	$\mathrm{E}[a_1^8]$	$\mathrm{E}[a_1^{10}]$	$\mathrm{E}[a_1^{12}]$	$\mathrm{E}[a_2]$	$\mathrm{E}[a_2^2]$	$\mathrm{E}[a_2^3]$	$\mathrm{E}[a_2^4]$	$\mathrm{E}[a_2^5]$	$\mathrm{E}[a_2^6]$	$\mathrm{E}[a_3^2]$	$\mathrm{E}[a_3^4]$	$\mathrm{E}[a_3^6]$	Maximal	Rational	Diagonal
1.2.B.1.1a	$1$	$2$	$1$	$\mathrm{U}(1)$	$\mathrm{U}(1)$	$1$	$0$	$2$	$6$	$20$	$70$	$252$	$252$											✓
1.4.B.1.1a	$1$	$4$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)$	$\mathrm{SU}(2)\times\mathrm{SU}(2)$	$1$	$0$	$2$	$10$	$70$	$588$	$5544$	$5544$	$2$	$5$	$14$	$44$	$152$	$569$					✓	$[1, 2, 2, 3, 4, 3, 4, 6, 6, 4]$
1.4.C.2.1a	$1$	$4$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)$	$N(\mathrm{U}(1)\times\mathrm{SU}(2))$	$2$	$0$	$2$	$11$	$90$	$889$	$9723$	$9723$	$2$	$5$	$14$	$46$	$172$	$714$				✓	✓	$[1, 2, 2, 4, 5, 4, 6, 11, 11, 6]$
1.4.D.2.1a	$1$	$4$	$2$	$\mathrm{U}(1)\times\mathrm{U}(1)$	$F_{ab}$	$2$	$1/2$	$2$	$18$	$200$	$2450$	$31752$	$31752$	$2$	$6$	$20$	$82$	$372$	$1824$					✓	$[1, 2, 3, 8, 12, 10, 14, 37, 40, 22]$
1.4.D.4.2a	$1$	$4$	$2$	$\mathrm{U}(1)\times\mathrm{U}(1)$	$F_{a,b}$	$4$	$1/4$	$2$	$12$	$110$	$1260$	$16002$	$16002$	$2$	$5$	$14$	$49$	$202$	$944$				✓	✓	$[1, 2, 2, 5, 6, 6, 8, 19, 22, 12]$
1.4.E.2.1a	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$E_2$	$2$	$1/2$	$2$	$16$	$160$	$1792$	$21504$	$21504$	$1$	$6$	$17$	$78$	$322$	$1516$					✓	$[1, 2, 5, 6, 10, 14, 10, 29, 28, 30]$
1.4.E.2.1b	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$J(E_1)$	$2$	$1/2$	$2$	$16$	$160$	$1792$	$21504$	$21504$	$2$	$6$	$20$	$78$	$332$	$1516$					✓	$[1, 2, 3, 6, 10, 8, 10, 25, 28, 16]$
1.4.E.3.1a	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$E_3$	$3$	$0$	$2$	$12$	$110$	$1204$	$14364$	$14364$	$1$	$4$	$13$	$52$	$222$	$1014$					✓	$[1, 2, 3, 4, 8, 6, 8, 17, 20, 12]$
1.4.E.4.1a	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$E_4$	$4$	$1/4$	$2$	$12$	$100$	$1008$	$11424$	$11424$	$1$	$4$	$11$	$46$	$182$	$824$					✓	$[1, 2, 3, 4, 6, 8, 6, 15, 16, 16]$
1.4.E.6.2a	$1$	$4$	$3$	$\mathrm{SU}(2)_{2}$	$E_6$	$6$	$1/6$	$2$	$12$	$100$	$980$	$10584$	$10584$	$1$	$4$	$11$	$44$	$172$	$754$					✓	$[1, 2, 3, 4, 6, 6, 6, 13, 12, 12]$
1.4.F.4.1a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$C_{4,1}$	$4$	$3/4$	$2$	$24$	$320$	$4480$	$64512$	$64512$	$1$	$5$	$22$	$115$	$606$	$3314$					✓	$[1, 2, 4, 9, 20, 16, 26, 77, 92, 52]$
1.4.F.4.2a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_2$	$4$	$3/4$	$2$	$24$	$320$	$4480$	$64512$	$64512$	$1$	$6$	$22$	$118$	$606$	$3324$					✓	$[1, 2, 5, 10, 20, 20, 26, 79, 92, 60]$
1.4.F.4.2b	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(C_2)$	$4$	$3/4$	$2$	$24$	$320$	$4480$	$64512$	$64512$	$1$	$7$	$22$	$123$	$606$	$3346$					✓	$[1, 2, 6, 11, 20, 26, 26, 83, 92, 78]$
1.4.F.4.2c	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_{2,1}$	$4$	$3/4$	$2$	$24$	$320$	$4480$	$64512$	$64512$	$2$	$7$	$26$	$123$	$622$	$3346$					✓	$[1, 2, 4, 11, 20, 18, 26, 77, 92, 54]$
1.4.F.6.1a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_3$	$6$	$1/2$	$2$	$18$	$220$	$3010$	$43092$	$43092$	$1$	$5$	$17$	$85$	$421$	$2263$					✓	$[1, 2, 4, 7, 14, 14, 18, 53, 62, 41]$
1.4.F.6.1b	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_{3,2}$	$6$	$1/2$	$2$	$18$	$220$	$3010$	$43092$	$43092$	$2$	$6$	$21$	$90$	$437$	$2285$					✓	$[1, 2, 3, 8, 14, 12, 18, 51, 62, 35]$
1.4.F.6.2a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(C_3)$	$6$	$1/2$	$2$	$18$	$220$	$3010$	$43092$	$43092$	$1$	$5$	$16$	$85$	$416$	$2264$					✓	$[1, 2, 4, 7, 14, 16, 18, 55, 62, 50]$
1.4.F.6.2b	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$C_{6,1}$	$6$	$1/2$	$2$	$18$	$220$	$3010$	$43092$	$43092$	$1$	$5$	$18$	$85$	$426$	$2264$					✓	$[1, 2, 4, 7, 14, 12, 18, 51, 62, 34]$
1.4.F.8.2a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(C_4)$	$8$	$5/8$	$2$	$18$	$200$	$2520$	$34272$	$34272$	$1$	$5$	$16$	$79$	$366$	$1904$					✓	$[1, 2, 4, 7, 12, 14, 14, 43, 48, 40]$
1.4.F.8.3b	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_4$	$8$	$5/8$	$2$	$18$	$200$	$2520$	$34272$	$34272$	$1$	$5$	$16$	$78$	$366$	$1898$					✓	$[1, 2, 4, 7, 12, 13, 14, 42, 48, 35]$
1.4.F.8.3c	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_{4,2}$	$8$	$5/8$	$2$	$18$	$200$	$2520$	$34272$	$34272$	$2$	$6$	$20$	$83$	$382$	$1920$					✓	$[1, 2, 3, 8, 12, 11, 14, 40, 48, 29]$
1.4.F.12.3a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$T$	$12$	$1/4$	$2$	$12$	$120$	$1540$	$21672$	$21672$	$1$	$4$	$12$	$52$	$236$	$1202$					✓	$[1, 2, 3, 4, 8, 8, 10, 27, 32, 22]$
1.4.F.12.4c	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_6$	$12$	$7/12$	$2$	$18$	$200$	$2450$	$31752$	$31752$	$1$	$5$	$16$	$77$	$356$	$1803$					✓	$[1, 2, 4, 7, 12, 12, 14, 39, 40, 29]$
1.4.F.12.4d	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$D_{6,2}$	$12$	$7/12$	$2$	$18$	$200$	$2450$	$31752$	$31752$	$2$	$6$	$20$	$82$	$372$	$1825$					✓	$[1, 2, 3, 8, 12, 10, 14, 37, 40, 23]$
1.4.F.12.5a	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$J(C_6)$	$12$	$7/12$	$2$	$18$	$200$	$2450$	$31752$	$31752$	$1$	$5$	$16$	$77$	$356$	$1804$					✓	$[1, 2, 4, 7, 12, 12, 14, 39, 40, 30]$
1.4.F.24.12b	$1$	$4$	$1$	$\mathrm{U}(1)_{2}$	$O$	$24$	$3/8$	$2$	$12$	$100$	$1050$	$12852$	$12852$	$1$	$4$	$11$	$45$	$181$	$837$					✓	$[1, 2, 3, 4, 6, 7, 6, 16, 18, 16]$
1.6.B.1.1a	$1$	$6$	$9$	$\mathrm{U}(3)$	$\mathrm{U}(3)$	$1$	$0$	$2$	$12$	$120$	$1610$	$25956$	$25956$	$1$	$4$	$18$	$107$	$743$	$5793$	$6$	$232$	$21260$		✓	$[1, 2, 3, 4, 4, 8, 9, 9, 12, 10, 6, 17, 22, 26, 40, 24, 19, 40, 30, 20]$
1.6.C.1.1a	$1$	$6$	$13$	$\mathrm{SU}(2)\times\mathrm{USp}(4)$	$\mathrm{SU}(2)\times \mathrm{USp}(4)$	$1$	$0$	$2$	$11$	$94$	$1050$	$14076$	$14076$	$2$	$6$	$23$	$109$	$613$	$3941$	$6$	$188$	$12226$	✓	✓	$[1, 2, 3, 2, 3, 6, 5, 6, 6, 3, 4, 9, 8, 12, 16, 8, 10, 12, 9, 4]$
1.6.D.2.1a	$1$	$6$	$11$	$\mathrm{U}(1)\times\mathrm{USp}(4)$	$N(\mathrm{U}(1)\times \mathrm{USp}(4))$	$2$	$0$	$2$	$12$	$114$	$1421$	$21195$	$21195$	$2$	$6$	$23$	$112$	$668$	$4656$	$6$	$198$	$15216$	✓	✓	$[1, 2, 3, 2, 4, 7, 6, 7, 7, 4, 6, 15, 13, 18, 25, 13, 13, 18, 15, 6]$
1.6.E.2.1a	$1$	$6$	$9$	$\mathrm{SU}(2)^3$	$E_{t}$	$2$	$0$	$2$	$13$	$145$	$2128$	$36624$	$36624$	$2$	$7$	$32$	$186$	$1287$	$10080$	$7$	$366$	$36795$		✓	$[1, 2, 4, 3, 4, 11, 11, 15, 16, 7, 6, 23, 25, 45, 70, 31, 40, 62, 41, 13]$
1.6.F.2.1a	$1$	$6$	$7$	$\mathrm{U}(1)\times\mathrm{SU}(2)^2$	$F_{at}$	$2$	$1/2$	$2$	$20$	$285$	$4949$	$97608$	$97608$	$2$	$8$	$44$	$308$	$2507$	$22530$	$9$	$692$	$90730$		✓	$[1, 2, 5, 3, 6, 22, 20, 25, 33, 12, 10, 61, 62, 122, 210, 87, 91, 179, 130, 31]$
1.6.F.4.2a	$1$	$6$	$7$	$\mathrm{U}(1)\times\mathrm{SU}(2)^2$	$F_{a,t}$	$4$	$1/4$	$2$	$14$	$165$	$2639$	$50253$	$50253$	$2$	$7$	$32$	$191$	$1402$	$11905$	$7$	$389$	$46510$	✓	✓	$[1, 2, 4, 3, 5, 12, 13, 17, 18, 10, 8, 33, 38, 64, 105, 51, 54, 97, 71, 24]$
1.6.G.4.1a	$1$	$6$	$5$	$\mathrm{U}(1)^2\times\mathrm{SU}(2)$	$F_{ac}\times \mathrm{SU}(2)$	$4$	$0$	$2$	$17$	$270$	$5439$	$123123$	$123123$	$2$	$7$	$38$	$284$	$2567$	$25820$	$7$	$658$	$111760$	✓	✓	$[1, 2, 4, 3, 6, 21, 21, 29, 38, 15, 13, 81, 85, 174, 310, 136, 146, 296, 229, 57]$
1.6.H.3.1a	$1$	$6$	$3$	$\mathrm{U}(1)^3$	$H_{s}$	$3$	$2/3$	$2$	$30$	$620$	$14910$	$390852$	$390852$	$1$	$7$	$61$	$615$	$6741$	$78043$	$12$	$1644$	$369720$		✓	$[1, 2, 6, 6, 9, 52, 52, 68, 114, 46, 32, 247, 284, 630, 1204, 562, 569, 1320, 1070, 294]$
1.6.H.4.1a	$1$	$6$	$3$	$\mathrm{U}(1)^3$	$H_{act}$	$4$	$1/2$	$2$	$24$	$470$	$11200$	$293202$	$293202$	$2$	$8$	$53$	$482$	$5117$	$58715$	$10$	$1254$	$277600$		✓	$[1, 2, 5, 4, 8, 38, 39, 54, 86, 35, 24, 188, 214, 474, 900, 424, 431, 990, 807, 218]$
1.6.H.8.2a	$1$	$6$	$3$	$\mathrm{U}(1)^3$	$H_{c,at}$	$8$	$3/8$	$2$	$18$	$290$	$6230$	$154602$	$154602$	$2$	$7$	$38$	$293$	$2822$	$30805$	$7$	$699$	$142000$	✓	✓	$[1, 2, 4, 3, 7, 22, 23, 33, 44, 20, 15, 101, 110, 240, 450, 215, 228, 498, 416, 112]$
1.6.I.4.2a	$1$	$6$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)_2$	$\mathrm{SU}(2)\times J(E_2)$	$4$	$0$	$2$	$16$	$235$	$4410$	$93744$	$93744$	$2$	$8$	$41$	$283$	$2362$	$22156$	$8$	$620$	$91760$		✓	$[1, 2, 5, 4, 6, 19, 20, 30, 36, 17, 11, 61, 69, 136, 235, 106, 122, 233, 170, 50]$
1.6.I.6.1a	$1$	$6$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)_2$	$\mathrm{SU}(2)\times J(E_3)$	$6$	$0$	$2$	$14$	$180$	$3136$	$64344$	$64344$	$2$	$7$	$33$	$210$	$1667$	$15215$	$7$	$442$	$62145$		✓	$[1, 2, 4, 3, 5, 14, 14, 21, 24, 11, 9, 42, 45, 92, 159, 70, 83, 151, 112, 30]$
1.6.I.8.3a	$1$	$6$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)_2$	$\mathrm{SU}(2)\times J(E_4)$	$8$	$0$	$2$	$14$	$175$	$2898$	$56364$	$56364$	$2$	$7$	$32$	$197$	$1502$	$13185$	$7$	$412$	$52590$	✓	✓	$[1, 2, 4, 3, 5, 13, 13, 19, 21, 11, 8, 37, 39, 75, 125, 58, 67, 121, 91, 28]$
1.6.I.12.4a	$1$	$6$	$6$	$\mathrm{SU}(2)\times\mathrm{SU}(2)_2$	$\mathrm{SU}(2)\times J(E_6)$	$12$	$0$	$2$	$14$	$175$	$2884$	$55314$	$55314$	$2$	$7$	$32$	$196$	$1482$	$12835$	$7$	$410$	$50735$	✓	✓	$[1, 2, 4, 3, 5, 13, 13, 18, 20, 10, 8, 36, 38, 69, 115, 51, 57, 102, 76, 23]$
1.6.J.4.2a	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J(J(E_2),E_2)$	$4$	$1/2$	$2$	$23$	$420$	$9331$	$229068$	$229068$	$2$	$9$	$56$	$471$	$4642$	$49891$	$10$	$1178$	$228360$		✓	$[1, 2, 6, 6, 10, 35, 41, 58, 80, 44, 20, 145, 184, 366, 688, 340, 336, 760, 599, 198]$
1.6.J.4.2b	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J(J(E_2),J(E_1))$	$4$	$1/2$	$2$	$23$	$420$	$9331$	$229068$	$229068$	$2$	$9$	$56$	$471$	$4642$	$49891$	$10$	$1178$	$228360$		✓	$[1, 2, 6, 4, 8, 35, 37, 52, 76, 32, 18, 145, 166, 364, 688, 318, 326, 722, 579, 150]$
1.6.J.6.1a	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J(J(E_3),E_3)$	$6$	$1/2$	$2$	$21$	$335$	$6797$	$159138$	$159138$	$2$	$8$	$45$	$348$	$3267$	$34220$	$8$	$828$	$154420$		✓	$[1, 2, 5, 4, 9, 26, 28, 40, 54, 25, 17, 102, 117, 245, 466, 219, 227, 485, 395, 105]$
1.6.J.8.3a	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J(J(E_4),J(E_2))$	$8$	$1/4$	$2$	$15$	$225$	$4739$	$114933$	$114933$	$2$	$7$	$35$	$257$	$2392$	$25195$	$8$	$630$	$114920$		✓	$[1, 2, 4, 4, 6, 18, 22, 31, 41, 25, 11, 74, 94, 187, 344, 175, 171, 382, 304, 104]$
1.6.J.8.3b	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J(J(E_4),E_4)$	$8$	$1/2$	$2$	$21$	$330$	$6419$	$142548$	$142548$	$2$	$8$	$44$	$329$	$2962$	$29790$	$8$	$762$	$129760$		✓	$[1, 2, 5, 4, 9, 25, 26, 37, 46, 26, 16, 93, 104, 202, 368, 182, 181, 392, 316, 104]$
1.6.J.8.5a	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J_2(J(E_2))$	$8$	$3/8$	$2$	$17$	$255$	$5131$	$119973$	$119973$	$2$	$8$	$41$	$291$	$2582$	$26276$	$8$	$662$	$116840$		✓	$[1, 2, 5, 4, 7, 20, 23, 34, 41, 25, 13, 78, 96, 187, 344, 175, 178, 384, 309, 104]$
1.6.J.12.4a	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J(J(E_6),J(E_3))$	$12$	$1/3$	$2$	$15$	$195$	$3605$	$81333$	$81333$	$2$	$7$	$32$	$208$	$1767$	$17680$	$7$	$471$	$78750$		✓	$[1, 2, 4, 3, 6, 14, 16, 22, 28, 15, 10, 53, 61, 125, 233, 113, 117, 245, 202, 56]$
1.6.J.12.4b	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J_2(J(E_3))$	$12$	$1/4$	$2$	$15$	$200$	$3717$	$83223$	$83223$	$2$	$7$	$33$	$216$	$1822$	$18040$	$7$	$471$	$79070$		✓	$[1, 2, 4, 3, 6, 15, 16, 24, 28, 15, 11, 55, 62, 126, 233, 114, 121, 246, 204, 57]$
1.6.J.12.4c	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J(J(E_6),E_6)$	$12$	$1/2$	$2$	$21$	$330$	$6405$	$140868$	$140868$	$2$	$8$	$44$	$328$	$2932$	$29110$	$8$	$756$	$124500$		✓	$[1, 2, 5, 4, 9, 25, 26, 36, 44, 23, 16, 92, 102, 192, 340, 156, 161, 332, 257, 80]$
1.6.J.16.11a	$1$	$6$	$4$	$\mathrm{U}(1)\times\mathrm{SU}(2)_2$	$J_2(J(E_4))$	$16$	$5/16$	$2$	$15$	$195$	$3479$	$74193$	$74193$	$2$	$7$	$32$	$203$	$1647$	$15685$	$7$	$438$	$66580$	✓	✓	$[1, 2, 4, 3, 6, 14, 15, 22, 24, 16, 10, 50, 55, 105, 184, 96, 97, 199, 165, 57]$